I am new to the Mathematica I want to Produce the Lagrange Inversion Coefficients by using Bell Polynomials.[![enter image description here][1]][1]
In the following image you can see 7 Coefficients which is calculated.
You can also see the An formula for calculating these coefficients by using Bell Polynomials.
Bn-1,k is the Bell Polynomial.
I want to produce the coefficients more than A7 I don't know how many times I should go further it depends on how much it converges to my result.
I believe it won't be hard to producing them but I have few knowledge in Mathematica yet. 

  [1]: https://i.sstatic.net/Try8u.jpg